Ronald B. Crosier

Bio: Ronald B. Crosier is an academic researcher from Lynn University. The author has contributed to research in topics: CUSUM & Head start. The author has an hindex of 7, co-authored 8 publications receiving 1237 citations.

Multivariate generalizations of cumulative sum quality-control schemes

Abstract: This article presents the design procedures and average run lengths for two mulativariater cumulative sum (CUSUM) quality-control procedures. The first CUSUM procedure reduces each multivariate observation to a scalar and then forms a CUSUM of the scalars. The second CUSUM procedure forms a CUSUM vector directly from the observations. These two procedures are compared with each other and with the multivariate Shewhart chart. Other multivariate quality-control procedures are mentioned. Robustness, the fast initial response feature for CUSUM schemes, and combined Shewhart-CUSUM schemes are discussed.

Fast initial response for CUSUM quality-control schemes: give your CUSUM a head start

Abstract: The fast initial response (FIR) feature for cumulative sum (CUSUM) quality-control schemes permits a more rapid response to an initial out-of-control situation than does a standard CUSUM quality-control scheme. This feature is especially valuable at start-up or after a CUSUM has given an out-of-control signal. This article presents the average run length and the distribution of run length for CUSUM schemes with the FIR feature and compares FIR CUSUM schemes to standard CUSUM schemes. The comparisons show that if the process starts out in control, the fast initial response feature has little effect; however, if the process mean is not at the desired level, an out-of-control signal will be given faster when the FIR feature is used.

A new two-sided cumulative sum quality control scheme

Abstract: A new two-sided cumulative sum quality control scheme is proposed. The new scheme was developed specifically to be generalized to a multivariate cumulative sum quality control scheme. The multivariate version will be examined in a subsequent paper; this article evaluates the univariate version. A comparison of the conventional two-sided cumulative sum scheme and the proposed scheme indicates that the new scheme has slightly better properties (ratio of on-aim to off-aim average run lengths) than the conventional scheme. Steady state average run lengths are discussed. The new scheme and the conventional two-sided cumulative sum scheme have equivalent steady state average run lengths. Methods for implementing the fast initial response feature for the new cumulative sum scheme are given. A comparison of average run lengths for the conventional and proposed schemes with fast initial response features is also favorable to the new scheme. A Markov chain approximation is used to calculate the average run lengths ...

Robust cusum: a robustness study for cusum quality control schemes

Abstract: A standard CUSUM control scheme and four modified CUSUM control schemes are evaluated for robustness. The average run length (ARL) for each scheme is evaluated using a contaminated normal distribution, a distribution that has longer tails than the normal. A CUSUM control scheme that ignores the first suspected outlier, but gives an out-of-control signal for two successive outliers is found to perform well.

Mixture Experiments: Geometry and Pseudocomponents

Abstract: Constraints, in the form of upper and lower bounds, are often placed on the components of mixtures. These constraints restrict the size of the experimental region and may alter its shape. A transformation from the original components to new variables, called pseudocomponents, is typically used to reduce the ill conditioning created by the restricted size of the experimental region. If the experimental region is a simplex, the pseudocomponent transformation is also used to adapt standard designs to the experimental region. A new pseudocomponent transformation is introduced, and the conditions under which it is preferable to the usual pseudocomponent transformation are given. The effect of changing the constraints on both the size and shape of the experimental region is discussed.

Detection of abrupt changes: theory and application

Abstract: This book is downloadable from http://www.irisa.fr/sisthem/kniga/. Many monitoring problems can be stated as the problem of detecting a change in the parameters of a static or dynamic stochastic system. The main goal of this book is to describe a unified framework for the design and the performance analysis of the algorithms for solving these change detection problems. Also the book contains the key mathematical background necessary for this purpose. Finally links with the analytical redundancy approach to fault detection in linear systems are established. We call abrupt change any change in the parameters of the system that occurs either instantaneously or at least very fast with respect to the sampling period of the measurements. Abrupt changes by no means refer to changes with large magnitude; on the contrary, in most applications the main problem is to detect small changes. Moreover, in some applications, the early warning of small - and not necessarily fast - changes is of crucial interest in order to avoid the economic or even catastrophic consequences that can result from an accumulation of such small changes. For example, small faults arising in the sensors of a navigation system can result, through the underlying integration, in serious errors in the estimated position of the plane. Another example is the early warning of small deviations from the normal operating conditions of an industrial process. The early detection of slight changes in the state of the process allows to plan in a more adequate manner the periods during which the process should be inspected and possibly repaired, and thus to reduce the exploitation costs.

Exponentially weighted moving average control schemes: properties and enhancements

Abstract: Roberts (1959) first introduced the exponentially weighted moving average (EWMA) control scheme. Using simulation to evaluate its properties, he showed that the EWMA is useful for detecting small shifts in the mean of a process. The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done. In this article, we evaluate the properties of an EWMA control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value. A design procedure for EWMA control schemes is given. Parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process. In addition, several enhancements to EWMA control schemes are considered. These include a fast initial response feature that makes the EWMA control scheme more sensitive to start-up problems, a combined Shewhart EWMA that provides protection against both larg...